Associativity of recurrence multiplication

P. J. Grabner; A. Pethő; R. F. Tichy; G. J. Woeginger

doi:10.1016/0893-9659(94)90017-5

Associativity of recurrence multiplication

P. J. Grabner^*, A. Pethő, R. F. Tichy, G. J. Woeginger

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

An extension of Knuth's Fibonacci multiplication to recurrences G _k+d = a1G _k+d-1 + ⋯ + a _d G _k with a ₁ ≥ a ₂ ≥ ⋯ ≥ a _d \2>0 and "canonical" initial values G _k = a ₁ G _k-1 + a ₂ G _k-2 + ⋯ + a _k G ₀ + 1, 0 ≤ k < d is established. We prove associativity for this multiplication if a related parameter is chosen sufficiently large.

Original language	English
Pages (from-to)	85-90
Number of pages	6
Journal	Applied Mathematics Letters
Volume	7
Issue number	4
DOIs	https://doi.org/10.1016/0893-9659(94)90017-5
Publication status	Published - Jul 1994

Keywords

Digit expansions
Linear recurrences
Pisot numbers.
β-shift

ASJC Scopus subject areas

Applied Mathematics

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10.1016/0893-9659(94)90017-5

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title = "Associativity of recurrence multiplication",

abstract = " An extension of Knuth's Fibonacci multiplication to recurrences G k+d = a1G k+d-1 + ⋯ + a d G k with a 1 ≥ a 2 ≥ ⋯ ≥ a d \2>0 and {"}canonical{"} initial values G k = a 1 G k-1 + a 2 G k-2 + ⋯ + a k G 0 + 1, 0 ≤ k < d is established. We prove associativity for this multiplication if a related parameter is chosen sufficiently large.",

keywords = "Digit expansions, Linear recurrences, Pisot numbers., β-shift",

author = "Grabner, {P. J.} and A. Peth{\H o} and Tichy, {R. F.} and Woeginger, {G. J.}",

year = "1994",

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T1 - Associativity of recurrence multiplication

AU - Grabner, P. J.

AU - Pethő, A.

AU - Tichy, R. F.

AU - Woeginger, G. J.

PY - 1994/7

Y1 - 1994/7

N2 - An extension of Knuth's Fibonacci multiplication to recurrences G k+d = a1G k+d-1 + ⋯ + a d G k with a 1 ≥ a 2 ≥ ⋯ ≥ a d \2>0 and "canonical" initial values G k = a 1 G k-1 + a 2 G k-2 + ⋯ + a k G 0 + 1, 0 ≤ k < d is established. We prove associativity for this multiplication if a related parameter is chosen sufficiently large.

AB - An extension of Knuth's Fibonacci multiplication to recurrences G k+d = a1G k+d-1 + ⋯ + a d G k with a 1 ≥ a 2 ≥ ⋯ ≥ a d \2>0 and "canonical" initial values G k = a 1 G k-1 + a 2 G k-2 + ⋯ + a k G 0 + 1, 0 ≤ k < d is established. We prove associativity for this multiplication if a related parameter is chosen sufficiently large.

KW - Digit expansions

KW - Linear recurrences

KW - Pisot numbers.

KW - β-shift

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U2 - 10.1016/0893-9659(94)90017-5

DO - 10.1016/0893-9659(94)90017-5

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SN - 0893-9659

VL - 7

SP - 85

EP - 90

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 4

ER -

Associativity of recurrence multiplication

Abstract

Keywords

ASJC Scopus subject areas

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